Question

Cho biết \(\frac{a+b}{3}=\frac{b+c}{5}=\frac{c+a}{10}\).Tính giá trị của biểu thức:\(M=11a+20b-c+2017\)

Answer 1

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{a+b}{3}=\frac{b+c}{5}=\frac{c+a}{10}=\frac{a+b-b-c-c-a}{-12}=\frac{c}{6}\)

\(\Rightarrow\frac{a+b}{3}=\frac{c}{6}\Rightarrow\left(a+b\right).6=3c\Rightarrow6a+6b=3c\Rightarrow3a+3b=c\Rightarrow a+b=\frac{c}{3}\)

\(\frac{b+c}{5}=\frac{c}{6}\Rightarrow6b+6c=5c\Rightarrow6b=-c\Rightarrow b=\frac{-c}{6}\)

\(\frac{c+a}{10}=\frac{c}{6}\Rightarrow6c+6a=10c\Rightarrow6a=4c\Rightarrow3a=2c\Rightarrow a=\frac{2c}{3}\)

thay vào M ta có:

\(\frac{22c}{3}+\frac{-20c}{6}-c+2017=4c-c+2017=3c+2017\)

p/s: ko chắc :))